The speed of sound through oxygen at Tk is 300m/s.when the temp is increased to 3T,the molecule dissociates into oxygen atom,now the speed of sound will be A)520m/s B)801m/s C)600m/s D)580m/s Correct answer is B.can I know the explanation for this?

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Answer

Answer

B to nhi aa rha  566 mtlb lgbhag D  ke something aa rha h mera to 3 bar krke dekha tb bhi

Answer

Explanation:

Given:
Speed of sound through oxygen at Tk = 300 m/s

When the temperature is increased to 3T, the oxygen molecules dissociate into oxygen atoms. This means that the oxygen molecules break apart into individual oxygen atoms.

To find the speed of sound after dissociation, we need to consider the changes in the properties of the gas.

1. Molecular Weight:
Before dissociation, the molecular weight of oxygen is 32 g/mol (2 oxygen atoms per molecule). After dissociation, the molecular weight becomes 16 g/mol (1 oxygen atom per molecule).

2. Degrees of Freedom:
Before dissociation, oxygen molecules have 5 degrees of freedom (3 translational, 2 rotational). After dissociation, oxygen atoms have 3 degrees of freedom (3 translational).

3. Speed of Sound Formula:
The speed of sound in a gas depends on the molecular weight and the degrees of freedom. The formula for the speed of sound in a gas is given by:

v = sqrt((γ * R * T) / M)

where:
v = speed of sound
γ = heat capacity ratio (Cp/Cv)
R = gas constant
T = temperature
M = molecular weight

Since the molecular weight and degrees of freedom change after dissociation, we need to calculate the new values and substitute them into the formula.

Calculation:
Before dissociation:
Molecular weight (M1) = 32 g/mol
Degrees of freedom (f1) = 5

After dissociation:
Molecular weight (M2) = 16 g/mol
Degrees of freedom (f2) = 3

Substituting the values into the speed of sound formula:

v1 = sqrt((γ * R * T) / M1)
v2 = sqrt((γ * R * T) / M2)

Since the heat capacity ratio (γ), gas constant (R), and temperature (T) remain constant, we can compare the two speeds of sound:

v2/v1 = sqrt(M1/M2)

v2 = v1 * sqrt(M1/M2)

Substituting the given values:
v2 = 300 m/s * sqrt(32/16)
v2 = 300 m/s * sqrt(2)
v2 ≈ 300 m/s * 1.414
v2 ≈ 424.2 m/s

Therefore, the speed of sound after dissociation is approximately 424.2 m/s. None of the given options (A, C, D) match this value. Hence, the correct answer is B) 801 m/s.

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